On some deterministic dictionaries supporting sparsity

Details On some deterministic dictionaries supporting sparsity On some deterministic dictionaries supporting sparsity

2008-08-09

arxiv.org/abs/0808.1368v2

Special issue on sparsity, the Journal of Fourier Analysis and Applications, Vol. 14, 859-876, Dec. 2008

Computer Science

Information Theory

Accepted for publication in the special issue on sparsity (Editors: Albert Cohen, Ronald DeVore, Michael Elad, Anna Gilbert) o

Scientific paper

We describe a new construction of an incoherent dictionary, referred to as the oscillator dictionary, which is based on considerations in the representation theory of finite groups. The oscillator dictionary consists of order of p^5 unit vectors in a Hilbert space of dimension p, where p is an odd prime, whose pairwise inner products have magnitude of at most 4/sqrt(p). An explicit algorithm to construct a large portion of the oscillator dictionary is presented.

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